1874.] Adiabatics and Isothermals of Wetter. 457 



In the figure the point /3' is represented as further from C than M is ; 

 if, however, ft' lies between M and C, then the crossing point of the 

 isothermal and adiabatic must be substituted for that of the two adia- 

 batics ; and in any case the areas of the two loops formed by two adia- 

 batics and an isothermal which meets each of them twice are equal. 



This result will still hold if we suppose that the two points of inter- 

 section with one of the adiabatics coincide, i. e. that it is that one which 

 has contact of the second order with the isothermal ; whence it follows 

 that the areas of the loops formed by any adiabatic and an isothermal 

 which meets it twice are equal ; or, in other words, that 



If a body perform a cycle of operations which can be represented by 

 an adiabatic and an isothermal, it will on the whole do no useful work. 



If we now proceed to consider the shapes of the adiabatics and 

 isothermals of water near their points of section with the curve w r hich 

 is the second boundary between the regions in which addition of heat 

 causes respectively increase and diminution of volume, and which corre- 

 sponds for any given pressure to a local maximum as that already dis- 

 cussed does to a minimum volume, the applications of several of the 

 above remarks are too obvious to need any special comment ; but there is 

 one isothermal the relations of which to the adiabatics which intersect it 

 are of a very complex order, and to which therefore it may be well to 

 draw attention. The isothermals of water may be divided into two 

 classes, according as the pressure corresponding to the freezing-point is 

 or is not less than the maximum tension of aqueous vapour at the given 

 temperature. 



As a type of the first we may take the isothermal corresponding to 

 C., which is represented in fig. 2. The maximum tension of steam at 

 this temperature is 4*6 millims. ; and as this is less than the pressure at 

 the freezing-point, the vapour will be directly precipitated into ice, which 

 will in turn be converted into water, when the pressure amounts to 760 

 millims., the solid being thus intermediate between the gaseous and 

 liquid states. 



An isothermal of the second class is represented in fig. 3. In this 

 case the vapour is precipitated in the form of water ; and as the possi- 

 bility of the existence of water at the given temperature and pressure 

 proves that the freezing-point for the given pressure is below the tempe- 

 rature proper to the isothermal, and as any further increase of pressure 

 will tend still further to depress it, it is evident that the water-substance 

 can never exist in the solid state at the given temperature unless at very 

 great pressures contraction instead of expansion accompanies solidifica- 

 tion. There must, therefore, be some isothermal which is at once the 

 boundary and limiting form of these two classes ; and if considered as 

 belonging to the first, it will be that for which the portion CD disappears, 

 i. e. for which the pressures corresponding to the freezing- and boiling- 

 points are the same. 



2M2 



